Statistics.cpp 13.8 KB
Newer Older
1
2
3
// Includes
#include "MantidKernel/Statistics.h"

4
#include <algorithm>
Campbell, Stuart's avatar
Campbell, Stuart committed
5
6
#include <cfloat>
#include <cmath>
7
#include <iostream>
Campbell, Stuart's avatar
Campbell, Stuart committed
8
9
#include <limits>
#include <numeric>
10
#include <sstream>
Campbell, Stuart's avatar
Campbell, Stuart committed
11
#include <stdexcept>
12
#include <functional>
Campbell, Stuart's avatar
Campbell, Stuart committed
13

Hahn, Steven's avatar
Hahn, Steven committed
14
15
16
17
18
#include <boost/accumulators/accumulators.hpp>
#include <boost/accumulators/statistics/min.hpp>
#include <boost/accumulators/statistics/max.hpp>
#include <boost/accumulators/statistics/variance.hpp>

19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
namespace Mantid {
namespace Kernel {

using std::string;
using std::vector;

/**
 * Generate a Statistics object where all of the values are NaN. This is a good
 * initial default.
 */
Statistics getNanStatistics() {
  double nan = std::numeric_limits<double>::quiet_NaN();

  Statistics stats;
  stats.minimum = nan;
  stats.maximum = nan;
  stats.mean = nan;
  stats.median = nan;
  stats.standard_deviation = nan;

  return stats;
}

/**
 * There are enough special cases in determining the median where it useful to
 * put it in a single function.
 */
template <typename TYPE>
double getMedian(const vector<TYPE> &data, const size_t num_data,
                 const bool sorted) {
  if (num_data == 1)
    return static_cast<double>(*(data.begin()));

Hahn, Steven's avatar
Hahn, Steven committed
52
  bool is_even = ((num_data & 1) == 0);
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
  if (is_even) {
    double left = 0.0;
    double right = 0.0;

    if (sorted) {
      // Just get the centre two elements.
      left = static_cast<double>(*(data.begin() + num_data / 2 - 1));
      right = static_cast<double>(*(data.begin() + num_data / 2));
    } else {
      // If the data is not sorted, make a copy we can mess with
      vector<TYPE> temp(data.begin(), data.end());
      // Get what the centre two elements should be...
      std::nth_element(temp.begin(), temp.begin() + num_data / 2 - 1,
                       temp.end());
      left = static_cast<double>(*(temp.begin() + num_data / 2 - 1));
      std::nth_element(temp.begin(), temp.begin() + num_data / 2, temp.end());
      right = static_cast<double>(*(temp.begin() + num_data / 2));
Campbell, Stuart's avatar
Campbell, Stuart committed
70
    }
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
    // return the average
    return (left + right) / 2.;
  } else
  // Odd number
  {
    if (sorted) {
      // If sorted and odd, just return the centre value
      return static_cast<double>(*(data.begin() + num_data / 2));
    } else {
      // If the data is not sorted, make a copy we can mess with
      vector<TYPE> temp(data.begin(), data.end());
      // Make sure the centre value is in the correct position
      std::nth_element(temp.begin(), temp.begin() + num_data / 2, temp.end());
      // Now return the centre value
      return static_cast<double>(*(temp.begin() + num_data / 2));
86
    }
87
  }
Hahn, Steven's avatar
Hahn, Steven committed
88
}
Hahn, Steven's avatar
Hahn, Steven committed
89

90
91
92
93
94
/**
 * There are enough special cases in determining the Z score where it useful to
 * put it in a single function.
 */
template <typename TYPE>
95
std::vector<double> getZscore(const vector<TYPE> &data) {
96
97
98
99
100
  if (data.size() < 3) {
    std::vector<double> Zscore(data.size(), 0.);
    return Zscore;
  }
  std::vector<double> Zscore;
101
  Statistics stats = getStatistics(data);
102
103
104
105
  if (stats.standard_deviation == 0.) {
    std::vector<double> Zscore(data.size(), 0.);
    return Zscore;
  }
Hahn, Steven's avatar
Hahn, Steven committed
106
  for (auto it = data.cbegin(); it != data.cend(); ++it) {
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
    double tmp = static_cast<double>(*it);
    Zscore.push_back(fabs((tmp - stats.mean) / stats.standard_deviation));
  }
  return Zscore;
}
/**
 * There are enough special cases in determining the modified Z score where it
 * useful to
 * put it in a single function.
 */
template <typename TYPE>
std::vector<double> getModifiedZscore(const vector<TYPE> &data,
                                      const bool sorted) {
  if (data.size() < 3) {
    std::vector<double> Zscore(data.size(), 0.);
    return Zscore;
  }
  std::vector<double> MADvec;
  double tmp;
  size_t num_data = data.size(); // cache since it is frequently used
  double median = getMedian(data, num_data, sorted);
Hahn, Steven's avatar
Hahn, Steven committed
128
  for (auto it = data.cbegin(); it != data.cend(); ++it) {
129
130
131
132
133
134
135
136
137
138
    tmp = static_cast<double>(*it);
    MADvec.push_back(fabs(tmp - median));
  }
  double MAD = getMedian(MADvec, num_data, sorted);
  if (MAD == 0.) {
    std::vector<double> Zscore(data.size(), 0.);
    return Zscore;
  }
  MADvec.clear();
  std::vector<double> Zscore;
Hahn, Steven's avatar
Hahn, Steven committed
139
  for (auto it = data.begin(); it != data.end(); ++it) {
140
141
142
143
144
145
146
147
148
    tmp = static_cast<double>(*it);
    Zscore.push_back(0.6745 * fabs((tmp - median) / MAD));
  }
  return Zscore;
}

/**
 * Determine the statistics for a vector of data. If it is sorted then let the
 * function know so it won't make a copy of the data for determining the median.
149
150
 * @param data Data points whose statistics are to be evaluated
 * @param flags A set of flags to control the computation of the stats
151
152
 */
template <typename TYPE>
153
Statistics getStatistics(const vector<TYPE> &data, const unsigned int flags) {
154
155
  Statistics stats = getNanStatistics();
  size_t num_data = data.size(); // cache since it is frequently used
156
  if (num_data == 0) {           // don't do anything
157
158
    return stats;
  }
159
160
161
  // calculate the mean if this or the stddev is requested
  const bool stddev = ((flags & StatOptions::UncorrectedStdDev) ||
                       (flags & StatOptions::CorrectedStdDev));
Hahn, Steven's avatar
Hahn, Steven committed
162
163
  if (stddev) {
    using namespace boost::accumulators;
Hahn, Steven's avatar
Hahn, Steven committed
164
    accumulator_set<TYPE, features<tag::min, tag::max, tag::variance>> acc;
Hahn, Steven's avatar
Hahn, Steven committed
165
166
    for (auto &value : data) {
      acc(value);
167
    }
Hahn, Steven's avatar
Hahn, Steven committed
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
    stats.minimum = min(acc);
    stats.maximum = max(acc);
    stats.mean = mean(acc);
    double var = variance(acc);

    if (flags & StatOptions::CorrectedStdDev) {
      double ndofs = static_cast<double>(data.size());
      var *= ndofs / (ndofs - 1.0);
    }
    stats.standard_deviation = std::sqrt(var);

  } else if (flags & StatOptions::Mean) {
    using namespace boost::accumulators;
    accumulator_set<TYPE, features<tag::mean>> acc;
    for (auto &value : data) {
      acc(value);
    }
    stats.mean = mean(acc);
186
  }
Hahn, Steven's avatar
Hahn, Steven committed
187

188
189
190
  // calculate the median if requested
  if (flags & StatOptions::Median) {
    stats.median = getMedian(data, num_data, flags & StatOptions::SortedData);
191
  }
Hahn, Steven's avatar
Hahn, Steven committed
192

193
194
195
196
197
198
  return stats;
}

/// Getting statistics of a string array should just give a bunch of NaNs
template <>
DLLExport Statistics
199
200
getStatistics<string>(const vector<string> &data, const unsigned int flags) {
  UNUSED_ARG(flags);
201
202
203
204
205
206
207
  UNUSED_ARG(data);
  return getNanStatistics();
}

/// Getting statistics of a boolean array should just give a bunch of NaNs
template <>
DLLExport Statistics
208
209
getStatistics<bool>(const vector<bool> &data, const unsigned int flags) {
  UNUSED_ARG(flags);
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
  UNUSED_ARG(data);
  return getNanStatistics();
}

/** Return the Rwp of a diffraction pattern data
  * @param obsI :: array of observed intensity values
  * @param calI :: array of calculated intensity values;
  * @param obsE :: array of error of the observed data;
  * @return :: RFactor including Rp and Rwp
  *
  */
Rfactor getRFactor(const std::vector<double> &obsI,
                   const std::vector<double> &calI,
                   const std::vector<double> &obsE) {
  // 1. Check
  if (obsI.size() != calI.size() || obsI.size() != obsE.size()) {
    std::stringstream errss;
    errss << "GetRFactor() Input Error!  Observed Intensity (" << obsI.size()
          << "), Calculated Intensity (" << calI.size()
          << ") and Observed Error (" << obsE.size()
          << ") have different number of elements.";
    throw std::runtime_error(errss.str());
  }
  if (obsI.size() == 0) {
    throw std::runtime_error("getRFactor(): the input arrays are empty.");
  }

  double sumnom = 0;
  double sumdenom = 0;
  double sumrpnom = 0;
  double sumrpdenom = 0;

  size_t numpts = obsI.size();
  for (size_t i = 0; i < numpts; ++i) {
    double cal_i = calI[i];
    double obs_i = obsI[i];
    double sigma = obsE[i];
    double weight = 1.0 / (sigma * sigma);
    double diff = obs_i - cal_i;

    if (weight == weight && weight <= DBL_MAX) {
      // If weight is not NaN.
      sumrpnom += fabs(diff);
      sumrpdenom += fabs(obs_i);

      double tempnom = weight * diff * diff;
      double tempden = weight * obs_i * obs_i;

      sumnom += tempnom;
      sumdenom += tempden;

      if (tempnom != tempnom || tempden != tempden) {
        std::cout << "***** Error! ****** Data indexed " << i << " is NaN. "
                  << "i = " << i << ": cal = " << calI[i] << ", obs = " << obs_i
                  << ", weight = " << weight << ". \n";
Campbell, Stuart's avatar
Campbell, Stuart committed
265
266
      }
    }
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
  }

  Rfactor rfactor(0., 0.);
  rfactor.Rp = (sumrpnom / sumrpdenom);
  rfactor.Rwp = std::sqrt(sumnom / sumdenom);

  if (rfactor.Rwp != rfactor.Rwp)
    std::cout << "Rwp is NaN.  Denominator = " << sumnom
              << "; Nominator = " << sumdenom << ". \n";

  return rfactor;
}

/**
 * This will calculate the first n-moments (inclusive) about the origin. For
 *example
 * if maxMoment=2 then this will return 3 values: 0th (total weight), 1st
 *(mean), 2nd (deviation).
 *
 * @param x The independent values
 * @param y The dependent values
 * @param maxMoment The number of moments to calculate
 * @returns The first n-moments.
 */
template <typename TYPE>
std::vector<double> getMomentsAboutOrigin(const std::vector<TYPE> &x,
                                          const std::vector<TYPE> &y,
                                          const int maxMoment) {
  // densities have the same number of x and y
  bool isDensity(x.size() == y.size());

  // if it isn't a density then check for histogram
  if ((!isDensity) && (x.size() != y.size() + 1)) {
    std::stringstream msg;
    msg << "length of x (" << x.size() << ") and y (" << y.size()
        << ")do not match";
    throw std::out_of_range(msg.str());
  }

  // initialize a result vector with all zeros
  std::vector<double> result(maxMoment + 1, 0.);

  // cache the maximum index
  size_t numPoints = y.size();
  if (isDensity)
    numPoints = x.size() - 1;

  // densities are calculated using Newton's method for numerical integration
315
316
  // as backwards as it sounds, the outer loop should be the points rather
  // than
317
318
319
320
321
322
323
324
325
  // the moments
  for (size_t j = 0; j < numPoints; ++j) {
    // reduce item lookup - and central x for histogram
    const double xVal = .5 * static_cast<double>(x[j] + x[j + 1]);
    // this variable will be (x^n)*y
    double temp = static_cast<double>(y[j]); // correct for histogram
    if (isDensity) {
      const double xDelta = static_cast<double>(x[j + 1] - x[j]);
      temp = .5 * (temp + static_cast<double>(y[j + 1])) * xDelta;
Campbell, Stuart's avatar
Campbell, Stuart committed
326
327
    }

328
329
330
331
332
    // accumulate the moments
    result[0] += temp;
    for (size_t i = 1; i < result.size(); ++i) {
      temp *= xVal;
      result[i] += temp;
333
    }
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
  }

  return result;
}

/**
 * This will calculate the first n-moments (inclusive) about the mean (1st
 *moment). For example
 * if maxMoment=2 then this will return 3 values: 0th (total weight), 1st
 *(mean), 2nd (deviation).
 *
 * @param x The independent values
 * @param y The dependent values
 * @param maxMoment The number of moments to calculate
 * @returns The first n-moments.
 */
template <typename TYPE>
std::vector<double> getMomentsAboutMean(const std::vector<TYPE> &x,
                                        const std::vector<TYPE> &y,
                                        const int maxMoment) {
  // get the zeroth (integrated value) and first moment (mean)
  std::vector<double> momentsAboutOrigin = getMomentsAboutOrigin(x, y, 1);
  const double mean = momentsAboutOrigin[1];

  // initialize a result vector with all zeros
  std::vector<double> result(maxMoment + 1, 0.);
  result[0] = momentsAboutOrigin[0];

  // escape early if we need to
  if (maxMoment == 0)
    return result;

  // densities have the same number of x and y
  bool isDensity(x.size() == y.size());

  // cache the maximum index
  size_t numPoints = y.size();
  if (isDensity)
    numPoints = x.size() - 1;

  // densities are calculated using Newton's method for numerical integration
375
376
  // as backwards as it sounds, the outer loop should be the points rather
  // than
377
378
379
380
381
382
383
384
385
386
387
388
389
390
  // the moments
  for (size_t j = 0; j < numPoints; ++j) {
    // central x in histogram with a change of variables - and just change for
    // density
    const double xVal =
        .5 * static_cast<double>(x[j] + x[j + 1]) - mean; // change of variables

    // this variable will be (x^n)*y
    double temp;
    if (isDensity) {
      const double xDelta = static_cast<double>(x[j + 1] - x[j]);
      temp = xVal * .5 * static_cast<double>(y[j] + y[j + 1]) * xDelta;
    } else {
      temp = xVal * static_cast<double>(y[j]);
391
392
    }

393
394
395
396
397
    // accumulate the moment
    result[1] += temp;
    for (size_t i = 2; i < result.size(); ++i) {
      temp *= xVal;
      result[i] += temp;
398
    }
399
400
401
402
403
404
405
406
407
  }

  return result;
}

// -------------------------- Macro to instantiation concrete types
// --------------------------------
#define INSTANTIATE(TYPE)                                                      \
  template MANTID_KERNEL_DLL Statistics                                        \
408
  getStatistics<TYPE>(const vector<TYPE> &, const unsigned int);               \
409
  template MANTID_KERNEL_DLL std::vector<double> getZscore<TYPE>(              \
410
      const vector<TYPE> &);                                                   \
411
412
413
414
415
416
417
418
419
420
421
  template MANTID_KERNEL_DLL std::vector<double> getModifiedZscore<TYPE>(      \
      const vector<TYPE> &, const bool);                                       \
  template MANTID_KERNEL_DLL std::vector<double> getMomentsAboutOrigin<TYPE>(  \
      const std::vector<TYPE> &x, const std::vector<TYPE> &y,                  \
      const int maxMoment);                                                    \
  template MANTID_KERNEL_DLL std::vector<double> getMomentsAboutMean<TYPE>(    \
      const std::vector<TYPE> &x, const std::vector<TYPE> &y,                  \
      const int maxMoment);

// --------------------------- Concrete instantiations
// ---------------------------------------------
422
423
424
425
426
427
428
429
INSTANTIATE(float)
INSTANTIATE(double)
INSTANTIATE(int)
INSTANTIATE(long)
INSTANTIATE(long long)
INSTANTIATE(unsigned int)
INSTANTIATE(unsigned long)
INSTANTIATE(unsigned long long)
430
431

} // namespace Kernel
432
} // namespace Mantid